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aliina [53]
3 years ago
10

the city wants to build a rectangular playground with an area of 1000 square feet or more. the length is 40 feet long. what are

the requirements for the width of the playground ?
Mathematics
1 answer:
kaheart [24]3 years ago
4 0
<h3>Answer: The width must be 25 feet or larger.</h3>

=================================================

Explanation:

x = width of the playground

x is some number which we don't know. Its basically a placeholder of sorts.

Multiply the width x by the length 40 to get x*40 = 40x

The area of the playground as an algebraic expression is 40x

We want this expression to be 1000 or larger, so we write this inequality 40x \ge 1000 (40x is greater than or equal to 1000)

Divide both sides by 40 and we end up with....

40x \ge 1000

\frac{40x}{40} \ge \frac{1000}{40}

x \ge 25

So x can be equal to 25, or it can be larger than 25.

In short, x must be at least 25 feet

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Answer:

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4 years ago
"If x is not &gt; 0, then x^2 is not &gt; 10" is the: -
Elanso [62]
<span>If </span><span /><span><span><span><span><span><span>x</span><span>≠</span><span><span><span>0</span></span></span></span><span /></span></span><span /></span><span>x≠0</span></span><span>, then </span><span /><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>x</span><span /></span><span><span>2</span><span /></span></span></span></span><span /></span><span><span><span><span>−</span><span /></span><span><span>−</span><span /></span></span><span /></span><span><span><span>√</span></span><span /></span></span></span><span /></span><span><span>x</span><span /></span><span><span /><span /></span></span></span><span>=</span></span><span /></span></span><span /></span><span>x2x=</span></span>
7 0
3 years ago
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func
olga2289 [7]

Answer:

a. C(1,000) = 420,491.11

b. c(1,000) = 420.49

c. dC/dx(1,000) = 429.72

d. x = 900

e. c(900) = 420

Step-by-step explanation:

We have a cost function for x units written as:

C(x) = 54,000 + 240x + 4x^{3/2}

a. The total cost for x=1000 units is:

C(1,000) = 54,000 + 240(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=54,000+240,000+4\cdot  31,622.78\\\\C(1,000)=54,000+240,000+ 126,491.11 \\\\C(1,000)=  420,491.11

b. The average cost c(x) can be calculated dividing the total cost by the amount of units:

c(1,000)=\dfrac{C(1,000)}{1,000}=\dfrac{ 420,491.11 }{1,000}= 420.49

c. The marginal cost can be calculated as the first derivative of the cost function:

\dfrac{dC}{dx}=240(1)+4(3/2)x^{3/2-1}=240+6x^{1/2}\\\\\\\dfrac{dC}{dx}(1,000)=240+6(1,000)^{1/2}=240+6\cdot 31.62=429.72

d. This value for x, that minimizes the average cost, happens when the first derivative of the average cost is equal to 0.

c(x)=\dfrac{C(x)}{x}=\dfrac{54,000+240x+4x^{3/2}}{x}=54,000x^{-1}+240+4x^{1/2}\\\\\\ \dfrac{dc}{dx}=54,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\\\\dfrac{dc}{dx}=-54,000x^{-2}+2x^{-1/2}=0\\\\\\2x^{-1/2}=54,000x^{-2}\\\\\\x^{-1/2+2}=54,000/2=27,000\\\\\\x^{3/2}=27,000\\\\\\x=27,000^{2/3}=900

e. The minimum average cost is:

c(900)=54,000(900)^{-1}+240+4(900)^{1/2}\\\\c(900)=60+240+120\\\\c(900)=420

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Answer:

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Step-by-step explanation:

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250*.3=75

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Answer:

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